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Ionic Surfactant Aggregates in Saline Solutions: SodiumDodecyl Sulfate (SDS) in the Presence of Excess

Sodium Chloride (NaCl) or Calcium Chloride (CaCl2

)Maria Sammalkorpi, Mikko Karttunen, and Mikko Haataja

J. Phys. Chem. B, 2009, 113 (17), 5863-5870• DOI: 10.1021/jp901228v • Publication Date (Web): 03 April 2009

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http://pubs.acs.org/doi/full/10.1021/jp901228v

Ionic Surfactant Aggregates in Saline Solutions: Sodium Dodecyl Sulfate (SDS) in thePresence of Excess Sodium Chloride (NaCl) or Calcium Chloride (CaCl2)

Maria Sammalkorpi,*,† Mikko Karttunen,‡ and Mikko Haataja†

Department of Mechanical and Aerospace Engineering, Princeton UniVersity, Princeton, New Jersey 08544,and Department of Applied Mathematics, The UniVersity of Western Ontario, London, Ontario, Canada N6A 5B7

ReceiVed: February 10, 2009; ReVised Manuscript ReceiVed: March 2, 2009

The properties of sodium dodecyl sulfate (SDS) aggregates in saline solutions of excess sodium chloride(NaCl) or calcium chloride (CaCl2) ions were studied through extensive molecular dynamics simulationswith explicit solvent. We find that the ionic strength of the solution affects not only the aggregate size of theresulting anionic micelles but also their structure. Specifically, the presence of CaCl2 induces more compactand densely packed micelles with a significant reduction in gauche defects in the SDS hydrocarbon chains incomparison with NaCl. Furthermore, we observe significantly more stable salt bridges between the chargedSDS head groups mediated by Ca2+ than Na+. The presence of these salt bridges helps stabilize the moredensely packed micelles.

1. Introduction

Micellization is a self-assembly phenomenon that occurs insolutions of amphiphilic molecules (surfactants), proteins,peptides, and block copolymers.1 In aqueous solutions abovethe critical micellization concentration, surfactants form in-soluble crystals or micelles depending on temperature.2,3 Morecomplex phases, such as cubic or lamellar, may also occur.1,3-7

These self-assembling structures appear across a broad rangeof length scales8 and can be exploited in a myriad of applica-tions, such as nanocarriers in drug delivery,9,10 emulsions andfoams,11 and even nanolithography.1 Interestingly, in the caseof ionic surfactants, the concentration and type of excess saltprovides another means to control the aggregate structure andproperties.

A fundamental understanding of the physical mechanismswhich control self-assembly processes requires detailed, mi-croscopic level molecular information. Experimentally, extract-ing this information is very challenging due to the characteristiclength (∼20 nm) and time (∼1 µs) scales associated withsurfactant micelles. One of the most important issues iselectrostatics as many molecules become ionized in aqueoussolutions, and ions and the ionic strength of the solution largelycontrol the association and dissociation of molecules inmicelles.12-18 While it is tempting to subsume the excess saltdegrees of freedom into an effective screened interactionbetween the charged surfactants, it has been very recentlydemonstrated that such a mean-field picture does not quantita-tively capture the effect of excess salt on aggregate structure inthermal equilibrium.19 In this work, we examine the role ofelectrostatic interactions and the presence of excess salt on bothaggregate structure and dynamics by employing moleculardynamics simulations with explicit solvent and salt.

Molecular dynamics (MD) simulations provide a naturalmethod to study the interactions and the kinetic pathways ofself-assembly processes when the time and length scales are

not too large. Thus far, micellization has been studied mostlyby lattice and off-lattice coarse-grained models.20-28 Morerecently, atomistic studies with and without solvent haveemerged.29-39 Since characteristic equilibration times for micelleformation are on the order of microseconds or longer, most ofthese simulations start from a spherical or rodlike micelle witha predetermined number of detergent molecules.26,30,33,35,36,40

Such an approach provides valuable insight into detergentdynamics and micelle structure within that particular initialsetup, but the results implicitly contain the assumption that theglobal minimum energy configuration, that is, micellar shapeand aggregation number, is close to the initial configuration.Although computationally much more demanding, a randominitial configuration is a more natural approach as it relaxes theabove limitations. Marrink et al.32 studied the micellization of54 dodecylphosphocholine (DPC) molecules and reported aconcentration-dependent aggregate structure. In our previouswork we provided analyses of the temperature dependence ofsodium dodecyl sulfate (SDS) micellization through extensive(200 ns) MD simulations with atomistic detail and also sawconcentration dependence and evidence of rodlike micelles.37,38

Lazaridis et al.39 simulated 960 DPC molecules in an implicitenvironment providing to date the temporally most extensivemicellization data but without explicit solvent. Very recently,models that combine atomistic simulations and a thermodynamicapproach for micelle formation41 have emerged.

In this study, we focus on the effects of sodium chloride andcalcium chloride on micellar systems consisting of SDS. SDSis the archetypal and the most commonly used ionic surfactant.Its use in biochemistry dates back, at least, to the 1940s.42

Seminal work on its structure and phase behavior was performedby Cabane, Kekicheff, and co-workers in a series of papers inthe middle of the 1980s in which they established the importanceof fluctuations and that the pathway from a planar system torodlike micelles occurs through several intermediate morphol-ogies.4,5,43,44 The effects of ionic concentration on micelleformation have been of keen interest for more than 40 years,see, e.g., refs 14, 15, and 45-51, and ionic strength of thesolution has been demonstrated as a means to tailor the

* Corresponding author. E-mail: [email protected]. FormerlyM. Huhtala.

† Princeton University.‡ The University of Western Ontario.

J. Phys. Chem. B 2009, 113, 5863–5870 5863

10.1021/jp901228v CCC: $40.75 2009 American Chemical SocietyPublished on Web 04/03/2009

properties of such aggregates,17,18 for example, as nanocarriersin drug delivery.9

Our main findings can be summarized as follows. First, thepresence of either type of excess salt leads to larger micellaraggregates than in their absence, in agreement with experimentalobservations. Second, the aggregate structures are markedlydifferent in the cases of NaCl and CaCl2. Specifically, theaggregates appear much more compact in the case of CaCl2.The enhanced structural rigidity of the aggregates in the caseof CaCl2 is attributed to the formation of relatively long-lived(∼0.5 ns) and stable salt bridges between nearest-neighbor headgroups, mediated by the Ca2+ ions.

The rest of this paper is organized as follows. The next sectionis devoted to the description of the model, its parameters, andcomputational details. Then, in section 3 we summarize theresults in terms of aggregate kinetics and structure in thepresence of excess salt. Section 4 contains the discussion ofour results, while concluding remarks are presented in section5.

2. Methods

2.1. Computational Model. The Gromacs 3.3 simulationpackage52-54 with the united atom parametrization was employedfor the atomistic molecular dynamics (MD) simulations. Theenergies of the initial configurations were minimized with thesteepest descent method. After the initialization, all simulationswere performed in the NpT ensemble at p ) 1 bar using theweak coupling method for pressure and temperature control.55

The coupling times were set to 1.0 ps for pressure and 0.1 psfor temperature, and the temperatures of the solute, counterions,and solvent were controlled independently. The bond lengthsof the detergent molecules were constrained by the LINCSalgorithm56 and those of the water molecules by SETTLE.57

Time step of 2 fs was used in all of the simulations reportedhere. The Lennard-Jones interactions were cut off at 1 nm, andthe full particle-mesh Ewald method58 was employed for thelong-ranged electrostatic interactions; not fully accounting forthese long-ranged electrostatic interactions has been shown tolead to serious artifacts in the simulations of amphiphilicmolecules,59,60 and contrary to the rather common misconception,proper treatment of electrostatics is also computationally ef-ficient.61

The SDS parameters are not part of the standard Gromacsforce field. The parametrization employed in this work has beendiscussed and validated in detail in our previous work37 and isavailable for download at http://www.softsimu.org/downloads.sh-tml. The sodium, calcium, and chloride ions were described bythe Gromacs parameters; for a detailed discussion of ionicparameters, please see refs 62 and 63. The simple point charge(SPC) water model,64 which is consistent with the chosen forcefield, was adopted for the water molecules. Visualizations ofall molecular configurations were generated with VMD (visualmolecular dynamics).65 Since the micelle-forming systemsstudied here have typically multiple micelles, and micelleproperties are computed for a given micelle, the data analysisrelies on identifying to which micelle each SDS moleculebelongs. The micelle classification scheme is based on geo-metrical distance constraints and has been described in detailin ref 37. Where applicable, the error has been estimated as thestandard deviation of the data sample.

2.2. Simulated System. We have studied micellization ofSDS molecules in the presence of two different types of excesssalt (NaCl and CaCl2). The number of SDS molecules in allsimulations reported here was set to 400. Five extensive

simulations (I-V), each 200 ns in duration while differing inthe concentration and type of excess salt ions, were carried out.In these five simulations, I contained no excess salt, II containedadditional 400 NaCl, III 1200 NaCl, IV 400 CaCl2, and V 1200CaCl2 molecules. We note that an SDS molecule consists of anionized Na+ (the counterions which are released when SDS isimmersed in an aqueous solution) and the anionic dodecylsul-phate molecule, see Figure 1. Thus, even in the absence ofexcess salt, a solution of SDS contains free Na+ counterions.

The simulated systems contained between 21 776 (the systemwith an excess of 1200 CaCl2 molecules) and 25 371 (the systemwith no excess salt) water molecules; the number of watermolecules varies between the systems because we desired tomaintain the system volumes comparable in the simulations. Interms of concentrations, the above numbers correspond to anSDS concentration of 700 mM and NaCl/CaCl2 concentrationof 700 mM or 2.1 M in the ionic solutions.

Initially, the SDS molecules were placed randomly withinthe simulation box with the sodium counterions close to theSDS head groups, see Figure 1. After this, the simulation boxwas filled with water. In the simulations with excess salt, theions were introduced by replacing randomly chosen watermolecules. Subsequently, the total energy was minimized usingthe steepest descent algorithm. Temperature was maintained at323 K. The temperature was deliberately chosen to be higherthan the critical micellization temperature to facilitate aggregateformation. The first 30 ns of all the trajectories was consideredas initial micelle formation period and was thus not includedin the analysis. The remaining 170 ns was used for analysis.Specifically, although initial agglomeration takes place duringthe first 5 ns, see Figure 2, the micelle structure still evolves.Careful inspection of the micelle structural characteristics revealsthat they have stabilized after 30 ns (data not shown), but weemphasize that the state represented between 30 and 200 ns isstill evolving and is thus not an equilibrium state; finalequilibration would take place on a time scale much longer thanthat achievable by current MD simulations. Having said that,the simulations reported here provide important molecular scaleinformation about micelle structure and kinetics in the presenceof excess salt.

3. Results

In the simulations, the initial SDS aggregation occurs rapidly,within the first few nanoseconds of the simulation. Figure 2presents the aggregation numbers of the clusters as a function

Figure 1. Left: The SDS molecule, where yellow represents sulfur,red oxygen, and light blue methyl group. The sodium counterion isdisplayed in blue. Right: An example of a random initial configurationof the 0.7 M 400 SDS-molecule system, here without excess salt. Forclarity, the 25 371 water molecules are omitted from the visualization.

5864 J. Phys. Chem. B, Vol. 113, No. 17, 2009 Sammalkorpi et al.

of time. As expected, the presence of excess salt appears todrive the systems toward larger micelles which is in goodagreement with experimental observations.48 The effect is lessprominent for excess NaCl than for CaCl2, which is perhapsnot surprising, since Ca2+ is a divalent ion and thus the resultingionic strength of the solution is increased relative to NaCl. Theexcess ion type also affects aggregation dynamics: whereasmicelles in the presence of excess NaCl undergo rapid fluctua-tions in size and shape, CaCl2 reduces the magnitudes offluctuations in both quantities; an implication of the latter isthat the micellar aggregates appear more compact in the presenceof CaCl2 relative to the salt-free or excess NaCl systems. Thisdeduction is confirmed by a visual inspection of the finalconfigurations of the simulations presented in Figure 3: in thepresence of the Na+ counterions, or an excess of NaCl, themicelles appear disordered and fluctuate in shape, whereas theintroduction of CaCl2 drives the SDS to form more compactmicelles with a smoother surface. It is interesting to note thatthere is little difference between the micellar structural char-acteristics of the 0.7 M and 2.1 M CaCl2 systems. This can beattributed to the fact that even the smaller excess salt concentra-tion is sufficient to provide an effective screening of the SDSheadgroup charges. Furthermore, the Ca2+ ions participate inthe formation of relatively long-lived salt bridges between thehead groups. This will be discussed in more detail below.

3.1. Gauche Defects. To characterize the aforementionedstructural changes we calculated the gauche defect probabilityof the hydrocarbon chains in the molecules. The data, shownin Figure 4, reveals that it is the excess ion type which impactsthe gauche defect probability, while the probability depends onlyvery weakly, if at all, on salt concentration. Specifically, theaddition of excess NaCl does not affect the defect probability,while the presence of CaCl2 results in a lower defect probabilityrelative to the salt-free system due to more effective screeningof repulsive head-head interactions. Interestingly, the defectprobability is unaffected by changes in the CaCl2 concentrationat these elevated excess salt concentrations.

Another quantity closely related to the frequency of gauchedefects in SDS molecules is their average length, defined asthe linear separation between the sulfur atom and the C12-atom

at the end of the hydrocarbon chain. The data shown in Table1 is in line with the gauche defect data: the monovalent sodiumand chloride ions do not affect the length of the SDS molecule.However, the presence of divalent Ca2+ ions has a significanteffect: the average SDS length has increased. In the presenceof excess CaCl2, the micelles are thus more compact withsuppressed SDS conformational fluctuations, and undergo lesssevere shape fluctuations relative to the salt-free system andthe ones with excess NaCl.

3.2. Ionic Charge Distribution. Let us next discuss the ioniccharge distribution around the SDS head groups. Figure 5

Figure 2. Micelle size distribution as a function of time. Thecumulative size of the 6 largest micelles is plotted in the graphs.Occasionally, two micelles are classified as one if they are very closeto one another, or one crystalline cluster is classified as two if the crystalhas a stacking defect.

Figure 3. Examples of aggregate structures with and without excessions. For each system, the largest micelle at the end of the simulation,i.e., at 200 ns, is presented. The spheres represent the ions (blue, sodium;cyan, chloride; tan, calcium) while surrounding micelles and watermolecules have been omitted to facilitate visualization of the micelle.

Figure 4. Gauche defect probability for different sites along the SDShydrocarbon chain. The carbon site numbering starts from the C-atomnext to the SO4-headgroup and is plotted so that, for example, 2.5 refersto the bond between the second and third carbon atom in the chain.Nonpolar hydrogen atoms are treated as a compound with theneighboring carbon atom, and therefore, the horizontal axis ranges bondsfrom 2.5 to 10.5.

TABLE 1: Sodium Dodecyl Sulfate (SDS) Length L

system La (nm)

no excess salt 1.36 ( 0.07700 mM NaCl 1.35 ( 0.082.1 M NaCl 1.37 ( 0.06700 mM CaCl2 1.42 ( 0.012.1 M CaCl2 1.46 ( 0.02

a The length is reported as the average S-C12 distance. Standarddeviation was used to estimate the error.

Aggregates in Saline Solutions J. Phys. Chem. B, Vol. 113, No. 17, 2009 5865

displays the charge distribution measured as a function of theabsolute radial distance from the SDS headgroup S atom forthe salt-free and 700 mM excess NaCl or CaCl2 systems; thebehavior is similar in 2.1 M excess salt solutions. To minimizethe effects of periodicity and influence of neighboring micellesin the analysis, a given ion contributes only to the chargedistribution of the closest headgroup. Thus, we expect theresulting charge distributions to reflect those of widely separatedmicelles. The valency of the excess ion type has a very strongeffect on the ionic charge distribution. In particular, the dataclearly show that, when present, divalent Ca2+ ions dominatethe behavior: they displace the Na+ ions from the vicinity ofthe head groups almost entirely. Furthermore, the form of theCl- curves indicates the weak presence of an electric doublelayer, although the micellar surfaces are not well-defined. Thesmall peak observed between 0.35 and 0.4 nm in the sodiumcurves in the salt-free or excess NaCl systems is associated withthe first binding shell of the SDS model, as discussed in ref 37.The main Na+ ion condensation peak is centered approximatelyat 0.58 nm and provides the dominant headgroup screening dueto Na+ ions, see ref 37. The cumulative charge distributions,shown in Figure 6, reveal the differences between the Na+ andCa2+ ions more clearly: the presence of Ca2+ gives rise to amuch more rapid increase in charge density to screen thenegatively charged SDS head groups relative to Na+.

Whereas the preceding graphs describe the charge distribu-tions componentwise, Figure 7 presents the total cumulative

charge as a function of distance from the S atom in the SDSheadgroup. Taking into account the polar characteristics of thewater molecules, we observe that salt-free and excess NaClsystems are characterized by essentially identical charge dis-tributions. On the other hand, a marked change is observed whenCaCl2 is introduced: CaCl2 causes more rapid charge neutraliza-tion. That is, the first cumulative charge peak is lower than forthe systems that have only sodium as the positive ion. On theother hand, systems with CaCl2 exhibit several layers of charge;that is, more of the electric double layer can be observedespecially at 2.1 M CaCl2. Although the plot presenting the totalcharge including the polar water molecules does not show adifference between the salt-free and excess NaCl systems, adifference can be observed if the intrinsic charge distributionof water molecules is disregarded in the plot. As shown in theimage on the right of Figure 7, additional Na+ ions induce amore rapid neutralization of the headgroup charge. On the otherhand, the presence of CaCl2 causes an overshoot even afterexcluding the contribution of the water molecule orientation:recall that the SPC water model comprises a rigid three-bodymolecule with the hydrogens charged 0.41e while the oxygenhas a charge -0.82e.64 To correct the dipole moment, thehydrogen-oxygen-hydrogen angle is 109.47°. For the 2.1 MCaCl2 even a minimum after the overshoot peak is observedagain indicating some double layer formation.

Figure 5. Charge distribution calculated as a function of distance tothe S atom in the SDS headgroup.

Figure 6. Componentwise contribution to the charge distributioncalculated as a function of distance to the S atom in the SDS headgroup.The charge is calculated per headgroup. Note that the SDS headgrouphas a total charge of -1.0 e.


3.3. Salt Bridges. Salt bridges66,67 could be a plausibleexplanation for the structural difference between the micellesformed in solutions containing NaCl and CaCl2. To study thisaspect, we assessed the probability of a salt bridge of givenduration existing between nearest-neighbor (NN) SDS head-group pairs, see Figure 8.

A salt bridge was defined to exist when two headgroupS-atoms were bridged by a Na+ or Ca2+ ion.66,67 Morespecifically, if the same cation (Na+ or Ca2+) resides within adistance Rcut ) 0.72 nm from two NN SDS head groups, a saltbridge is formed between the head groups. The specific valuefor Rcut is based on the radial distribution functions correspond-ing to Na+ and Ca2+ condensation radii measured from theS-atoms in the headgroup. The same Rcut ) 0.72 nm valuecorresponding to Ca2+ condensation radius was employed forboth Na+ and Ca2+ ions, although the respective ion condensa-tion radius for Na+ is 0.675 nm, see ref 37; this is justified asthe outcome of the salt bridge analysis is only weakly sensitiveto the employed Rcut value. Specifically, as long as Rcut is chosensuch that only ions from the corresponding condensation shellscontribute to salt bridges, the results are unchanged.

Figure 8 shows that there are salt bridges in the system buttheir lifetimes are rather short, i.e., less than 1 ns. However,the probability distribution decays much faster for Na+ mediatedsalt bridges than for Ca2+ mediated bridges; Ca2+ mediated saltbridges typically have significantly longer lifetimes. This isdemonstrated by Table 2 which presents the average salt bridgelifetime for each system: Ca2+ mediated salt bridges are muchmore stable and have an average lifetime (e0.3 ns) that issignificantly larger than that of Na+ mediated ones (e0.1 ns).Furthermore, the presence of CaCl2 stabilizes the Na+ mediatedbridges making their average lifetime longer. The stabilizingrole of the Ca2+ mediated salt bridges can also be observed inthe S-S shortest distance distribution, i.e., the NN distancedistribution of the micelle head groups, shown in Figure 9. Thedata shows a sharper distribution peak for the CaCl2 containingsystems than for the systems with no excess salt or NaCl.Furthermore, the latter distributions are much broader incomparison to the CaCl2 containing systems, implying thepresence of larger structural fluctuations in the NaCl systems.Indeed, visual examination of the trajectories indicates that thedynamics of individual SDS species in the micelles is slowerand more constrained in the presence CaCl2. Additionally, thedistributions presented in Figure 9 show a small shift in thepeak position; that is, the most likely S-S NN distance isslightly smaller when CaCl2 is introduced in comparison to theNaCl containing systems. This is to be expected as the greaterscreening strength of the Ca2+ ions should allow for denserpacking of the head groups. However, with the studiedconcentrations, there is hardly any concentration dependencein the S-S NN distance distributions of the systems containingCaCl2. This is due to the short screening length with CaCl2;adding more CaCl2 does not have a significant effect at smallscales. However, the state of affairs is very different with smallconcentrations of NaCl: for the system with no excess salt andthe two different concentrations of excess NaCl, the distributioncan be seen to develop into a sharper peak as the concentrationof NaCl is increased.

We conclude that Na+ mediated salt bridges have such a shortaverage lifetime that they are unlikely to contribute to the overallstability and structure of SDS micelles but for the Ca2+ ionsthe salt bridges may play a key role in stabilizing the micelles.The salt bridge analysis also shows that although the micellesare effectively screened by the ions, i.e., have very smalleffective charges, ion condensation is dynamic, i.e., the ionsand head groups do not form permanent cation-anion pairs inthe solution at T ) 323 K.

It is interesting to note that we have observed strongindications of formation of rodlike micelles as the ionic strengthof the solution increases. Specifically, at elevated salt concentra-tions, SDS molecules pack densely enough such that theyeffectively adopt a more cylindrical (rather than conelike) shape.It is well-known that a cylindrical packing volume favors rodlikemicelles in comparison to spherical micelles, and thus, weconclude that an increase in the ionic strength eventually induces

Figure 7. Top: Cumulative charge as a function of distance to the Satom in the SDS headgroup including the point charges of the solvent.Bottom: Cumulative charge distribution due to counterions and excesssalt. Note that the SDS headgroup has a total charge of -1.0.

Figure 8. Probability of a salt bridge of given duration existing forany of the SDS head groups. The legend indicates the system and theion mediating the salt bridge. Please note that, in the presence of excessCaCl2, in addition to Ca2+ ions there are also the Na+ counterionscorresponding to the 0.7 M SDS concentration, and also, these maycontribute to salt bridge formation.

TABLE 2: Average Salt Bridge Lifetime

bridge ion systemaverage

lifetime (ns)

Na+ no excess salt 0.08Na+ 0.7 M NaCl 0.06Na+ 2.1 M NaCl 0.07Na+ 0.7 M CaCl2 0.10

Ca2+ 0.7 M CaCl2 0.21Na+ 2.1 M CaCl2 0.12

Ca2+ 2.1 M CaCl2 0.30


a transition from spherical to elongated and finally to rodlikemicelles. However, we are unable to probe this very interestingmorphological transition regime at this point, as it is beyondthe current capabilities of MD simulations.

4. Discussion

We have investigated the effect of monovalent and divalentions on the formation of micellar aggregates using large-scaleMD simulations with explicit solvent and salt. We observe saltbridges to play an important role in both stabilizing the micellesand increasing their size. Furthermore the presence of divalentCa2+ ions is observed to dominate ion condensation around themicelles, leading to more compact aggregates in comparisonwith the monovalent Na+.

In the 200 ns simulations performed in this work, we observemicelles with sizes from around 50 SDS to approximately 200SDS depending on the amount and type of excess salt in thesystem. Additionally, we see indications of rodlike micellarstructures as the ionic strength increases. Experimentally, it iswell-established that the aggregation number of ionic micellesgrows as a function of surfactant or ion concentration,68-72 andour results fully agree with these observations. At criticalmicellization concentration (8 ( 1.4 mM, depending onmeasurement),73-78 SDS forms micelles of size, i.e., aggregationnumber of 55-77 molecules69,70,78,75,47 at temperatures close tothe critical micellization temperature (CMT). Most of themeasurements have been performed at temperatures closer tothe CMT than in our simulations, in which the higher temper-ature facilitates more efficient exploration of micellizationkinetics. The micelles we observe are significantly larger,potentially rodlike aggregates than in experiments without excesssalt and the systems with excess salt.79,80,70,72 It should also benoted that both the SDS and excess salt concentrations employedin this study are quite large, especially compared to the CMC.It is interesting to note that ref 79 reports that an increasedtemperature causes the SDS micelles asymptotically to approacha spherical shape with a hydrated radius of about 25 Å nearlyindependently of NaCl or SDS concentration. We are not awareof systematic data regarding SDS micelle size in the presenceof multivalent ions at temperatures significantly above CMT.All in all, our observations are well in line with experimentalobservations: at the simulation temperature T ) 323 K, we seealmost spherical, slightly elongated micelles for the pure SDSsolution and the systems with excess NaCl. Significant differencein the structure is only introduced with the divalent Ca2+ forwhich the micelles become visibly elongated with flat areas andareas of high curvature showing signs of potential transformationto rodlike structure. Furthermore, the simulation descriptionrestricts our observations: The micelles, once formed, are in alocal energy minimum, and if the minimum is deep enough, itis unlikely that we see further size evolution within the sub-

microsecond time window we are able to examine. Additionally,the enlarged micelles present at high SDS concentrations or inthe presence of excess salt have been reported to be polydispersein size which indicates a rather small free energy differencebetween the aggregate sizes.3,81 We conclude that observedmicelle sizes provide a lower limit to the actual micelle sizesin experiments.

Besides the size of the micelle, we observe the type of excessions in the solution to influence the structure. In the presenceof CaCl2, Ca2+ replaces Na+ as the condensed counterion,micelles are significantly more ordered and compact, and thesurfactant molecules are effectively more rigid. Rigidity showsboth in the dynamics and in the molecule length, or gauchedefect probability. Ion interactions and their effects on dodecylsulfate micelles have been studied in refs 35, 72, 79, and 82-87.The general agreement is that the ion type and concentrationaffect the micelle structure and dynamics. Particularly fordodecyl sulfate, ref 86 reports selective counterion condensationfor sodium and lithium dodecyl sulfate in the presence of LiBrand NaBr; our observations of Ca2+ condensation dominanceare well in line with these observations. Reference 35 providesa comparison between lithium, sodium, and ammonium coun-terions. Multivalent ions have been studied much less: Theeffects of Na+, Ca2+, and Al3+ on sodium dodecyl polyoxyeth-ylene-2-sulfate micelles have been compared in ref 88 whereeven a small concentration of multivalent ions is reported tochange the micelle shape and increase the aggregation numberclose to CMT. The observations are again well in line with ourobservations of excess Ca2+ inducing much more drastic changesin micelle structure, aggregation, and dynamics than excess Na+.Additionally, Vasilescu et al.87 report that an increasing Al3+

concentration first increases the SDS micelle size, and thencauses precipitation, and when the Al3+ concentration is furtherincreased, the precipitate becomes soluted again as wormlikemicelles. This may happen with Ca2+ under proper conditionsas well, and the observations of first an increase in the micellesize and then a transition to rodlike micelles are consistent withour results on Ca2+, although we cannot conclude whether themicelles in our work are rodlike or elongated at high ionicconcentrations.

In addition to studies of micelle interaction with various ions,there exist also studies of ion interactions with lipid bilayers.89,90,67

Ion condensation, however, depends strongly on geometry.91

Reference 89 reports that sodium ions affect both the structureand dynamics of a lipid bilayer. We observe a much smallereffect in the case of anionic micelles: SDS structure is hardlyaffected by the excess NaCl, but micellization dynamicsbecomes faster as the process is driven by the ions. Reference90 shows that calcium becomes dominantly bound to lipidbilayers comprising POPC, and affects the structure. Our resultsagree with the observations: SDS micelles bind calcium strongly,and the structure of the micelles changes in the presence of thedivalent ions. References 89 and 90 also claim a long relaxationtime for the ions starting from the water phase with the presenceof a preformed lipid bilayer. In our simulations, both thesurfactants and ions form initially a random aqueous solutionwith the water molecules. As a result of this in our system thesurfactant relaxation, i.e., reaching micelle structure equilibrium,is the bottleneck: we emphasize that the configurations analyzedin this work are metastable configurations.

It is temptingtocompareourresultswiththePoisson-Boltzmanntheory.92,93 There is, however, a difficulty since it is not possibleto uniquely determine the surface of a micelle as would berequired by the theory. In addition, the surface is atomistic.

Figure 9. S-S nearest neighbor distance distribution.


Strictly speaking, the Poisson-Boltzmann theory is valid onlyin the case of a smooth structureless surface. Such a fit has beenperformed, however, for a planar atomistic lipid bilayer byGurtovenko et al.94 Since it is easier to determine the surfaceplane for a bilayer, the authors were able to fit the chargedistribution and compare with the Poisson-Boltzmann (orGouy-Chapman, to be precise) theory in the case of a charged(cationic) lipid bilayer and no added salt. The simulation resultsand theory were in found to be in excellent agreement. Withadded salt, such as the case here, a different treatment isneeded.92,93

Finally, in ref 67 ionic binding and Na+ mediated ion bridgeswere demonstrated to play a key role in anionic lipid bilayers.This supports our finding of a large number of salt bridges inthe ionic micelles, although we observe the Na+ mediatedbridges to be short, typically tens of picoseconds in duration.Ca2+, however, forms salt bridges that are more stable andsignificantly longer in duration, hundreds of picoseconds, whichmakes these bridges a significant contribution to the micellestructure in the presence of Ca2+ ions.

5. Conclusions

In conclusion, we reported here the behavior of SDS micellesin the presence of excess NaCl or CaCl2. The results show thatsalt, especially the divalent CaCl2, can be used as a means tomanipulate micelle properties. Specifically, our main findingscan be summarized as follows. First, the presence of eitherexcess salt leads to larger micellar aggregates than in its absence.Second, the aggregate structures are markedly different in thecases of NaCl and CaCl2. For the latter, the aggregates appearmuch more compact. Third, the enhanced structural rigidity ofthe aggregates in the case of CaCl2 arises from relatively long-lived (∼0.5 ns) salt bridges between nearest-neighbor headgroups, mediated by the Ca2+ ions.

Acknowledgment. This work has been supported by theNatural Sciences and Engineering Research Council of Canada(M.K.), and through NSF-DMR Grant 0449184 (M.H.). We alsothank the Southern Ontario SharcNet (www.sharcnet.ca) com-puting facility for computer resources.

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